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Problem 527 from Connelly's corpus: Ha, Hc, N


Problem

Given a point Ha, a point Hc and a point N, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Hc and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Hc and N are not the same

  2. Choose freely a point Ha on the circle k(N,Ma) (rule WOncircle)

  3. Using the point Ha and the point Hc, construct a line m(HaHc) (rule W14);

    % DET: points Ha and Hc are not the same

  4. Using the circle k(N,Ma) and the line m(HaHc), construct a point Mb and a point Eb (rule W04);

    % NDG: line m(HaHc) and circle k(N,Ma) intersect

  5. Choose freely a point A on the circle k(Mb,C) (rule WOncircle)

  6. Using the point A and the point Mb, construct a point C (rule W01);

  7. Using the point A and the point Ha, construct a line ha (rule W02);

    % DET: points A and Ha are not the same

  8. Using the point Hc and the point C, construct a line hc (rule W02);

    % DET: points Hc and C are not the same

  9. Using the line ha and the line hc, construct a point H (rule W03);

    % NDG: lines ha and hc are not parallel

    % DET: lines ha and hc are not the same

  10. Using the point N and the point H, construct a point G (rule W01);

  11. Using the point Mb and the point G, construct a point B (rule W01);

animation
Construction in GCLC language

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